MD80 Captain experienced a cabin altitude warning shortly after leveling off at FL340. An emergency descent was initiated with diversion to nearest suitable airport.

Narrative

Approximately 10 minutes after leveloff at FL340 the red CABIN ALTITUDE overhead light illuminated -- the red MASTER WARNING lights illuminated -- aural cabin altitude alert sounded. Verified cabin altimeter indicated 10K+100-200 FT -- immediately complied with emergency procedure -- turned seatbelt sign on -- made PA instructing all passengers and cabin crew to be seated and fasten seatbelts. Coordinated for and initiated immediate descent with Center as emergency aircraft. Descent granted initially to 14000 FT. Spoke with flight attendants on intercom -- briefed emergency memory items and queried regarding passengers/flight attendants all seated. Instructed flight attendants to comply with emergency landing checklist based upon 10 miles to landing. Cabin altitude during entire descent indicated 10K+100/200 to 10K-500/700 FT. Oxygen masks had not been auto-deployed nor deployed by cockpit crew. Complied with descent checklist and began Mechanical Before Landing Checklist early. Coordinated with Center to relay emergency info and request CFR be at runway of intended landing. Initiated communications with Tower early and ensured CFR was on Tower frequency. Instructed CFR to meet aircraft at midfield upon stopping and check entire aircraft for any signs of damage or pending danger and then followed the aircraft to the gate. Complied with After Landing checklist. Deplaned at gate upon arrival.